New algorithms for one-loop integrals

Oldenborgh, G. J. van; Vermaseren, J. A. M.

doi:10.1007/bf01621031

Cited by 476 publications

(478 citation statements)

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“…VA in [14]). In four dimensions, shifting the integration variables in (44), one can obtain the standard representation of the three-point function in terms of dilogarithms [28] (see also in [29]). …”

Section: One Gluon On Shell P 2 3 =mentioning

confidence: 99%

Quark mass dependence of the one-loop three-gluon vertex in arbitrary dimension

Davydychev

Osland

Saks

2001

J. High Energy Phys.

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Section: One Gluon On Shell P 2 3 =mentioning

confidence: 99%

Quark mass dependence of the one-loop three-gluon vertex in arbitrary dimension

Davydychev

Osland

Saks

2001

J. High Energy Phys.

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“…The basic approach has been modified in a variety of ways, including the introduction of a system of (n − 1) reciprocal vectors v µ i (and the associated second rank tensor w µν playing the role of g µν ) to carry the tensor structure [3,4,5] where, This simplifies the identification of the formfactor coefficients, but does not eliminate the Gram determinants. In fact, in both approaches, the number of Gram determinants generated is equal to the number of loop momenta in the numerator of the original integral.…”

Section: Introductionmentioning

confidence: 99%

One-loop tensor integrals in dimensional regularisation

1997

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We show how to evaluate tensor one-loop integrals in momentum space avoiding the usual plague of Gram determinants. We do this by constructing combinations of nand (n − 1)-point scalar integrals that are finite in the limit of vanishing Gram determinant. These non-trivial combinations of dilogarithms, logarithms and constants are systematically obtained by either differentiating with respect to the external parameters -essentially yielding scalar integrals with Feynman parameters in the numerator -or by developing the scalar integral in D = 6 − 2ǫ or higher dimensions. An additional advantage is that other spurious kinematic singularities are also controlled. As an explicit example, we develop the tensor integrals and associated scalar integral combinations for processes where the internal particles are massless and where up to five (four massless and one massive) external particles are involved. For more general processes, we present the equations needed for deriving the relevant combinations of scalar integrals.

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“…(A.15) and (A.17), we get 19) which provides two equations (one for each tensor structure) that determine the coefficients f and c. Calculating the (finite) integrals we find f = 1 18 and c = − 1 3 . For four-point basic functions, which are at most logarithmically singular, the situation is similar.…”

Section: A1 Massless Basic Functionsmentioning

confidence: 99%